Problem: Simplify the following expression: $y = \dfrac{q}{5} + \dfrac{q}{10}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5$ and $10$ $\lcm(5, 10) = 10$ $ y = \dfrac{2}{2} \cdot \dfrac{q}{5} + \dfrac{1}{1} \cdot \dfrac{q}{10} $ $y = \dfrac{2q}{10} + \dfrac{q}{10}$ $y = \dfrac{2q +q}{10}$ $y = \dfrac{3q}{10}$